This is an announcement for the paper "An extension of a Bourgain--Lindenstrauss--Milman inequality" by Omer Friedland and Sasha Sodin.
Abstract: Let || . || be a norm on R^n. Averaging || (\eps_1 x_1, \cdots, \eps_n x_n) || over all the 2^n choices of \eps = (\eps_1, \cdots, \eps_n) in { -1, +1 }^n, we obtain an expression ||| . ||| which is an unconditional norm on R^n. Bourgain, Lindenstrauss and Milman showed that, for a certain (large) constant \eta > 1, one may average over (\eta n) (random) choices of \eps and obtain a norm that is isomorphic to ||| . |||. We show that this is the case for any \eta > 1.
Archive classification: math.FA math.PR
The source file(s), kkh_18.6.tex: 12943 bytes, is(are) stored in gzipped form as 0706.2638.gz with size 5kb. The corresponding postcript file has gzipped size 63kb.
Submitted from: sodinale@post.tau.ac.il
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/0706.2638
or
http://arXiv.org/abs/0706.2638
or by email in unzipped form by transmitting an empty message with subject line
uget 0706.2638
or in gzipped form by using subject line
get 0706.2638
to: math@arXiv.org.